We sat him down and told him we are not going to remind him anymore because we feel like we are doing his thinking for him and not letting him take responsibility for his own work. Is this the route to take? What should the consequences be if he doesn't start keeping track of his school work? We don't want to just leave him hanging and have his grades drop.
If you have been "constantly reminding" your son about his homework responsibilities, he is probably going to have a tough transition to doing it solely on his own. Not because he can't be responsible in this manner, but because he has gotten into the habit of letting you be responsible for this part of his school life.
Rather than saying that you are not going to do this for him anymore and letting him suffer the consequences, speak with his teacher and hear her recommendations for helping him be more mindful of his homework assignments. Then sit down with your son and discuss ideas for helping him become successful in this arena -- a chart of daily assignments posted in his room, a note that his teacher tapes to his coat before he leaves school, a list of the books he needs to take home, etc.
Write down all the suggestions, perhaps initially giving more importance to his suggestions than to yours or his teacher's, and then draft a written plan. Have him carry this plan with him at all times, have it posted in his room, and be sure the teacher has a copy. Agree to check in with each other at least twice a week to see how the plan is working and offer appropriate encouragement for any success that he is achieving.
He may falter initially because this is a new set of responsibilities. Rather than focusing on the negative consequences of what will befall him if he does not initially respond well, talk in an ongoing, encouraging manner about how he will soon have a "foolproof master plan" in place so that this will no longer be an issue. Point out all improvements and go back to the drawing board as many times as it takes to fine-tune the plan and celebrate its increasing success.
It certainly helps to have the teacher on board as his and your ally.